Homework 1: One-sample Hypothesis Testing with known population variance
1. Test the claim that the true mean diameter of a manufactured bolt is 30mm. Assume population
standard deviation equals 0.8mm. Tolerate type I error =0.05. A sample of 100 bolts is collected.
The sample mean is 29.84. Please use both the P-value method and the critical value method to
test your understanding of the two methods.
Answer to question 1 with critical value method
1. The value of interest is
30mm
2. State the appropriate null and alternative hypotheses
H0: µ=30 H1: µ≠30 This is a two tail test
3. Specify the desired level of significance
Suppose that = 0.05
4. (only when using critical value method) Determine the critical values
For = 0.05 the critical Z values are ±1.96 (two tails, two values)
The null use the equal sign, so the level of significance is divided by 2, and assigned
equally to the left and the right side.
5. Determine the appropriate test statistic
σ is assumed known so this is a Z test.
Compute the test statistic according to the sample information
2.0
.160
μX
ZSTAT −=
−
=
−
=
−
=
